During the past two years, through our own work as well as by others, considerable progress has been made in understanding the genetic epidemiology and pathogenesis of triplet repeat loci which cause disease in expanded form. However, the mechanism of initiation of this expansion is not well understood. Our own work indicates that mutation at alleles in the normal size range contribute significantly to allele pools of the "premutation" stage, and that such mutation mechanism(s) can, in general, be formulated as a Generalized Stepwise Mutation Model (GSMM). Further, we showed that the natural history of triplet repeat diseases depends on population-related factors. Our study produced a mathematical tool, the Coalescent with Markov Mutations (CMM), which is capable of modeling this phenomenon. We propose to study the analytical and computational properties of the CMM\ when used to analyze data on allele size distributions at disease-causing triplet repeat polymorphisms, in normal individuals as well as in carrier and affected individuals. Specifically, our models will incorporate the impact of past demographic changes and the evolutionary history of human populations. Our aims are: (i) to detect the presence of allele-size expansion/contraction mutation bias for alleles in the normal size range and, if bias exists, to examine its affect on the frequency of "premutation" alleles at these loci, (ii) to detect allele size dependence of mutation rates, and (iii) to examine the role of natural selection in the maintenance of "normal" repeat-size variation of alleles. Models developed under these aims will be used as follows: (iv) to study the impact of population-related factors and (v) to design statistical tests and to conduct power computations for hypotheses testing. Finally, (vi) we will assess the impact of these factors on the predictive utility of "premutation" alleles for disease frequency estimation and on sample size requirements for disease screening. The anticipated results of this study should provide insight into the ancestry of disease-causing mutations as well as into the conditions under which disease prevalence can be maintained. These refined models and their applications to world-wide data should also explain how the molecular heterogeneity of triplet repeats affects disease progression.